Optimal. Leaf size=28 \[ a e^2 x+\frac {2}{5} a e f x^5+\frac {1}{9} a f^2 x^9 \]
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Rubi [A] time = 0.01, antiderivative size = 28, normalized size of antiderivative = 1.00, number of steps used = 3, number of rules used = 2, integrand size = 11, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.182, Rules used = {12, 194} \[ a e^2 x+\frac {2}{5} a e f x^5+\frac {1}{9} a f^2 x^9 \]
Antiderivative was successfully verified.
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Rule 12
Rule 194
Rubi steps
\begin {align*} \int a \left (e+f x^4\right )^2 \, dx &=a \int \left (e+f x^4\right )^2 \, dx\\ &=a \int \left (e^2+2 e f x^4+f^2 x^8\right ) \, dx\\ &=a e^2 x+\frac {2}{5} a e f x^5+\frac {1}{9} a f^2 x^9\\ \end {align*}
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Mathematica [A] time = 0.00, size = 27, normalized size = 0.96 \[ a \left (e^2 x+\frac {2}{5} e f x^5+\frac {f^2 x^9}{9}\right ) \]
Antiderivative was successfully verified.
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fricas [A] time = 0.60, size = 24, normalized size = 0.86 \[ \frac {1}{9} x^{9} f^{2} a + \frac {2}{5} x^{5} f e a + x e^{2} a \]
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.14, size = 25, normalized size = 0.89 \[ \frac {1}{45} \, {\left (5 \, f^{2} x^{9} + 18 \, f x^{5} e + 45 \, x e^{2}\right )} a \]
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.04, size = 24, normalized size = 0.86 \[ \left (\frac {1}{9} f^{2} x^{9}+\frac {2}{5} e f \,x^{5}+e^{2} x \right ) a \]
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 1.37, size = 25, normalized size = 0.89 \[ \frac {1}{45} \, {\left (5 \, f^{2} x^{9} + 18 \, e f x^{5} + 45 \, e^{2} x\right )} a \]
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 4.67, size = 25, normalized size = 0.89 \[ \frac {a\,x\,\left (45\,e^2+18\,e\,f\,x^4+5\,f^2\,x^8\right )}{45} \]
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.12, size = 27, normalized size = 0.96 \[ a e^{2} x + \frac {2 a e f x^{5}}{5} + \frac {a f^{2} x^{9}}{9} \]
Verification of antiderivative is not currently implemented for this CAS.
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